SurfaceContourPlot3D

SurfaceContourPlot3D[f, p ∈ reg]

generates a contour plot of f over the surface of the three-dimensional region reg, treating f as a function of the point p.

Examples

Color a sphere by the values of x y:

SurfaceContourPlot3D[x y, {x, y, z} ∈ Sphere[]]

Display a legend for the contour values:

SurfaceContourPlot3D[x + z, {x, y, z} ∈ Torus[], PlotLegends -> Automatic]

See the official Wolfram Language reference for options and supported regions.